Biomedical subjects
Publications and source records attributed to Hrvoje Buljan.
We show that two Bloch modes launched into a nonlinear photonic lattice evolve into a comb or a supercontinuum of spatial frequencies, exhibiting a sensitive dependence on the difference between the quasi-momenta of the two initially excited modes. This phenomenon results from four-wave mixing combined with exchanges of momentum between the optical field and the lattice.
We report what is to our knowledge the first experimental observation of gap random-phase lattice solitons: self-trapped spatially incoherent entities whose modal constituents lie within a photonic bandgap.
We predict random-phase spatial solitons in instantaneous nonlocal nonlinear media. The key mechanism responsible for self-trapping of such incoherent wave packets is played by the nonlocal (rather than the traditional noninstantaneous) nature of the nonlinearity. This kind of incoherent soliton has profoundly different features than other incoherent solitons.
We present a novel, real-time, experimental technique for linear and nonlinear Brillouin zone spectroscopy of photonic lattices. The method relies on excitation with random-phase waves and far-field visualization of the spatial spectrum of the light exiting the lattice. Our technique facilitates mapping the borders of the extended Brillouin zones and the areas of normal and anomalous dispersion within each zone. For photonic lattices with defects (e.g., photonic crystal fibers), our technique enables far-field visualization of the defect mode overlaid on the extended Brillouin zone structure of the lattice. The technique is general and can be used for photonic crystal fibers as well as for periodic structures in areas beyond optics.
The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or 'discrete') solitons; these have been studied in many branches of science. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.
We present the first experimental observation of modulation instability and spontaneous pattern formation with incoherent white light emitted from an incandescent light bulb. We show experimentally that modulation instability of white light propagating in a noninstantaneous self-focusing medium is a collective effect, where the entire temporal spectrum of the light beam becomes unstable at the same threshold value and collectively forms a pattern with a single periodicity. We experimentally demonstrate that the temporal spectrum of the evolving perturbation self-adjusts to match the collective pattern formation phenomenon.
We study the propagation dynamics of an incoherent light beam circulating in a passive cavity containing noninstantaneous nonlinear media. It is shown that patterns form in this cavity in spite of spatial incoherence of the light. We show that the pattern formation process is always associated with two consecutive thresholds. The first (instability) threshold is unaffected by the cavity boundary conditions, whereas the second threshold is induced by the feedback through the interplay of nonlinear gain and cavity loss.
Optical spatial solitons made from incoherent white light were experimentally observed in 1997 by Mitchell and Segev [Nature (London) 387, 880 (1997)]. We present what is believed to be the first theory describing these solitons and find the characteristic features of their spatiotemporal coherence properties and their temporal power spectrum.
We develop a theory describing propagation of spatially and temporally incoherent light in noninstantaneous nonlinear media, and predict the existence of modulation instability of "white" light. We find that the modulation instability of white light is fundamentally a collective effect, where all the temporal frequencies participate in the formation of a pattern, and self-adjust their respective contributions.
We study local and global correlations between the naturally invariant measure of a chaotic one-dimensional map f and the conditionally invariant measure of the transiently chaotic map f(H). The two maps differ only within a narrow interval H, while the two measures significantly differ within the images f(l)(H), where l is smaller than some critical number l(c). We point out two different types of correlations. Typically, the critical number l(c) is small. The chi(2) value, which characterizes the global discrepancy between the two measures, typically obeys a power-law dependence on the width epsilon of the interval H, with the exponent identical to the information dimension. If H is centered on an image of the critical point, then l(c) increases indefinitely with the decrease of epsilon, and the chi(2) value obeys a modulated power-law dependence on epsilon.